Yona accidentally wounded Zeno with her arrow in the recent chapters, it slashed his left shoulder
The dripping sound is the blood trickling down Zeno’s left hand from the wound in his shoulder and THAT’S what Zeno is shocked about! That the wound hasn’t healed! He understood that it was never about the sword, it’s about Yona - Hiryuu. She can give him real wounds and, therefore, kill him with anything at all.
Even his brand new neck wound from the sword healed instantly, but not the shoulder one.